Surface effect on the phonon transport of silicon nanowire

Thermal conductance measurements are presented on nanostructured individual single crystalline Si suspended nanowires at low temperature. The mechanically suspended silicon nanowires with different sizes (130nm by 100nm and 130 nm by 200nm) are fabricated by e-beam lithography from Silicon On Insulator (SOI) substrate. The thermal conductance of the ballistic phonon wave guides is measured by means of an ac technique, the 3 ω method, using a niobium nitride transducer deposited on top. The geometry of the nanowire is chosen to match the order of magnitude of the dominant phonon wave length in silicon at low temperature which is of the order of 100 nm at 1K. A regular cubic law is observed at high temperature, but a deviation is measured at the lowest temperature with a saturation of thermal conductance which is attributed to the reduced geometry of the nanowire. The experimental results are in agreement with the Casimir theory taking into account the surface state (roughness) of the silicon wire. The deviation observed at low temperature is a clear signature of the consequence of the low dimentionality of the wire as well as the surface effects on the phonon transport